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Algorithmic logic. Multiple-valued extensions

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Abstract

Extended algorithmic logic (EAL) as introduced in [18] is a modified version of extended ω+-valued algorithmic logic. Only two-valued predicates and two-valued propositional variables occur in EAL. The role of the ω+-valued logic is restricted to construct control systems (stacks) of pushdown algorithms whereas their actions are described by means of the two-valued logic. Thus EAL formalizes a programming theory with recursive procedures but without the instruction CASE.

The aim of this paper is to discuss EAL and prove the completeness theorem. A complete formalization of EAL was announced in [20] but no proof of the completeness theorem was given.

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Rasiowa, H. Algorithmic logic. Multiple-valued extensions. Stud Logica 38, 317–335 (1979). https://doi.org/10.1007/BF00370471

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